# RBS Theory

Rutherford Backscattering (RBS) is based on collisions between atomic nuclei and derives its name from Lord Ernest Rutherford, who in 1911 was the first to present the concept of atoms having nuclei. It involves measuring the number and energy of ions in a beam which backscatter after colliding with atoms in the near-surface region of a sample at which the beam has been targeted.

With this information, it is possible to determine atomic mass and elemental concentrations versus depth below the surface. RBS is ideally suited for determining the concentration of trace elements heavier than the major constituents of the substrate. Its sensitivity for light masses, and for the makeup of samples well below the surface, is poor.

When a sample is bombarded with a beam of high energy particles, the vast majority of particles are implanted into the material and do not escape. This is because the diameter of an atomic nucleus is on the order of 1e-15 m while the spacing between nuclei is on the order of 2e-10 m. A small fraction of the incident particles do undergo a direct collision with a nucleus of one of the atoms in the upper few micrometers of the sample. This "collision" does not actually involve direct contact between the projectile ion and target atom. Energy exchange occurs because of Coulombic forces between nuclei in close proximity to each other. However, the interaction can be modeled accurately as an elastic collision using classical physics.

The energy measured for a particle backscattering at a given angle depends upon two processes. Particles lose energy while they pass through the sample, both before and after a collision. The amount of energy lost is dependent on that material's stopping power. A particle will also lose energy as the result of the collision itself. The collisional lost depends on the masses of the projectile the target atoms. The ratio of the energy of the projectile before and after collision is called the kinematic factor.

The number of backscattering events that occur from a given element in a sample depend upon two factors: the concentration of the element and the effective size of its nucleus. The probability that a material will cause a collision is called its scattering cross section.